Bond lengths, harmonic vibrational frequencies and dissociation energies of TlAt are calculated at ab initio molecular orbital and density functional theory using effective spin-orbit operator and relativistic effective core potentials. Spin-orbit effects estimated from density functional theory are in good agreement with those from ab initio calculations, implying that density functional theory with effective core potentials can be an efficient and reliable methods for spin-orbit interactions. The estimated R-e, omega(e), and D-e values are 2.937 Angstrom, 120 cm(-1), 1.96 eV for TlAt. Spin-orbit effects generally cause the bond contraction in Group 13 elements and the bond elongation in the Group 17 elements, and spin-orbit effects on R-e of TlAt are almost cancelled out. The spin-orbit effects on D-e of TlAt are roughly the sum of spin-orbit effects on D-e of the corresponding element hydrides. Electron correlations and spin-orbit effects are almost additive in the TlAt molecule.